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arXiv:1609.07707 · Physical Review A

Structure, branching ratios, and a laser-cooling scheme for the BaF138 molecule

Tao Chen, Wenhao Bu, Bo Yan

Published Dec 19, 2016• 54 citations
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Abstract

For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable ${A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}$ and ${A}^{2}\mathrm{\ensuremath{\Pi}}$ states and, further, the lifetime of the $\mathrm{\ensuremath{\Delta}}$ state have been estimated since the loss procedure via the $\mathrm{\ensuremath{\Delta}}$ state might fatally break the main quasicycling $\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and $g$ factors for both $X$ and $A$ states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.

DOI
10.1103/physreva.94.063415

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Spectroscopic characterization of aluminum monofluoride with relevance to laser cooling and trapping

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arXiv:1908.11774•Physical Review A•Nov 26, 2019•59 citations
For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable A\ensuremath′2\ensuremathΔ{A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}A\ensuremath′2\ensuremathΔ and A2\ensuremathΠ{A}^{2}\mathrm{\ensuremath{\Pi}}A2\ensuremathΠ states and, further, the lifetime of the \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ state have been estimated since the loss procedure via the \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ state might fatally break the main quasicycling \ensuremathΣ\ensuremath−\ensuremathΠ\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}\ensuremathΣ\ensuremath−\ensuremathΠ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the X2\ensuremathΣ+{X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}X2\ensuremathΣ+ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and ggg factors for both XXX and AAA states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.
More recently, laser cooling of the diatomic radical magnesium monofluoride (24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F. Meanwhile, we also calculate the accurate hyperfine structure magnetic ggg factors of the rotational state ($X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$, and lighter mass, the 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.
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Recently, there have been great interest and advancement in the field of laser cooling and magneto-optical trapping of molecules. The rich internal structure of molecules naturally lends themselves to extensive and exciting applications. In this paper, the radical , as a promising candidate for laser cooling and magneto-optical trapping, is discussed in detail. The highly diagonal Franck–Condon factors between the and states are first confirmed with three different methods. Afterwards, with the effective Hamiltonian approach and irreducible tensor theory, the hyperfine structure of the state is calculated accurately. A scheme for laser cooling is given clearly. Besides, the Zeeman effects of the upper ( ) and lower ( ) levels are also studied, and their respective g factors are obtained under a weak magnetic field. Its large g factor of the upper state is advantageous for magneto-optical trapping. Finally, by studying Stark effect of BaF in the , we investigate the dependence of the internal effective electric field on the applied electric field. It is suggested that such a laser-cooled BaF is also a promising candidate for precision measurement of electron electric dipole moment.
We demonstrate buffer-gas cooling, high-resolution spectroscopy, and cycling fluorescence of cold barium monofluoride (BaF) molecules. Our source produces an intense and internally cold molecular beam containing the different BaF isotopologues with a mean forward velocity of 190m/s190\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}190m/s. For a well-collimated beam of 138Ba19F^{138}\mathrm{Ba}\phantom{\rule{0.16em}{0ex}}^{19}\mathrm{F}138Ba19F we observe a flux of >1010>{10}^{10}>1010 molecules ${\mathrm{sr}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{pulse}}^{\ensuremath{-}1}$ in the $X{\phantom{\rule{0.16em}{0ex}}}^{2}\mathrm{\ensuremath{\Sigma}}$, N=1N=1N=1 state in our downstream detection region. Studying the absorption line strength of the intermediate ${A}^{\ensuremath{'}}\mathrm{\ensuremath{\Delta}}$ state we infer a lifetime of ${\ensuremath{\tau}}_{\mathrm{\ensuremath{\Delta}}}=790\ifmmode\pm\else\textpm\fi{}346\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, significantly longer than previously estimated. Finally, highly diagonal Franck-Condon factors and magnetic remixing of dark states allow us to realize a quasicycling transition in 138Ba19F^{138}\mathrm{Ba}\phantom{\rule{0.16em}{0ex}}^{19}\mathrm{F}138Ba19F that is suitable for future laser cooling of this heavy diatomic molecule.
The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He2∗_2^*2∗​ would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck-Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin-rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He2∗_2^*2∗​ molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He2∗_2^*2∗​. The sensitivity of the vibrational levels of He2+_2^+2+​ with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.
Here we report on spectroscopic measurements of the aluminum monofluoride molecule (AlF; boson) that are relevant to laser cooling and trapping experiments. We measure the detailed energy-level structure of AlF in the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic ground state, in the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state, and in the metastable $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ state. We determine the rotational, vibrational, and electronic branching ratios from the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state. We also study how the rotational levels split and shift in external electric and magnetic fields. We find that AlF is an excellent candidate for laser cooling on any QQQ line of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ - $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ transition and for trapping at high densities. The energy levels in the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},v=0$ state and within each $\mathrm{\ensuremath{\Omega}}$ manifold in the $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},v=0$ state are determined with a relative accuracy of a few kHz, using laser-radio-frequency multiple resonance and ionization detection schemes in a jet-cooled, pulsed molecular beam. To determine the hyperfine and $\mathrm{\ensuremath{\Lambda}}$-doubling parameters we measure transitions throughout the 0.1-MHz--66-GHz range, between rotational levels in the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},v=0$ state, and between rotational and $\mathrm{\ensuremath{\Lambda}}$-doublet levels in all three spin-orbit manifolds of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},v=0$ state. We measure the hyperfine splitting in the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state using continuous wave (cw) laser-induced fluorescence spectroscopy of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0\ensuremath{\leftarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},{v}^{\ensuremath{''}}=0$ band. The resolution is limited by the short radiative lifetime of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0$ state, which we experimentally determine to be $1.90\ifmmode\pm\else\textpm\fi{}0.03$ ns. The hyperfine mixing of the lowest rotational levels in the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state causes a small loss from the main laser cooling transition of ${10}^{\ensuremath{-}5}$. The off-diagonal vibrational branching from the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0$ state is measured to be $(5.60\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in good agreement with theoretical predictions. The strength of the spin-forbidden $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0\ensuremath{\rightarrow}a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},{v}^{\ensuremath{'}}=0$ transition is measured to be seven orders of magnitude lower than the strength of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},{v}^{\ensuremath{''}}=0$ transition. We determine the electric dipole moments $\ensuremath{\mu}(\mathrm{X})=1.515\ifmmode\pm\else\textpm\fi{}0.004$ Debye, $\ensuremath{\mu}(a)=1.780\ifmmode\pm\else\textpm\fi{}0.003$ Debye and $\ensuremath{\mu}(\mathrm{A})=1.45\ifmmode\pm\else\textpm\fi{}0.02$ Debye in $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$, v=0v=0v=0, $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},v=0$ and $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0$, respectively, by recording cw laser excitation spectra in electric fields up to 150 kV/cm.